A278525 Filtering sequence (related to prime factorization): a(n) = A046523(A241916(n)).

1, 2, 2, 4, 2, 4, 2, 8, 6, 4, 2, 8, 2, 4, 6, 16, 2, 12, 2, 8, 6, 4, 2, 16, 6, 4, 12, 8, 2, 12, 2, 32, 6, 4, 6, 24, 2, 4, 6, 16, 2, 12, 2, 8, 12, 4, 2, 32, 6, 12, 6, 8, 2, 36, 6, 16, 6, 4, 2, 24, 2, 4, 12, 64, 6, 12, 2, 8, 6, 12, 2, 48, 2, 4, 30, 8, 6, 12, 2, 32, 24, 4, 2, 24, 6, 4, 6, 16, 2, 36, 6, 8, 6, 4, 6, 64, 2, 12, 12, 24, 2, 12, 2, 16, 30, 4, 2, 72, 2

Offset: 1

Author

Antti Karttunen, Nov 30 2016

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000040, A046523, A241916, A278220, A278221.

Programs

PARI

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A209229(n) = (n && !bitand(n,n-1));
A241916(n) = if(1==A209229(n), n, my(f = factor(2*n), nbf = #f~, igp = primepi(f[nbf,1]), g = f); for(i=1,nbf,g[i,1] = prime(1+igp-primepi(f[i,1]))); factorback(g)/2);
A278525(n) = A046523(A241916(n)); \\ Antti Karttunen, Jul 02 2018

Scheme

(define (A278525 n) (A046523 (A241916 n)))

Formula

a(n) = A046523(A241916(n)).

Other identities. For all n:

a(2^n) = 2^n.

a(A000040(n)) = 2.